Turning to FIG. 1, an example of a conventional communication system 100 can be seen. In this system 100, there is a transmitter 102 and a receiver 104 that each employ direct conversion circuitry, although superheterodyne circuitry can also employed. For the transmitter 102, there is a modulator (which generally includes phase adjustment circuit 108-1 (which can, for example, be a hybrid) and mixers 106-1 and 106-2) and local oscillator 110-1 that receives in-phase (I) and quadrature (Q) signals from baseband circuitry 112-1 and upconverts these signals to a radio frequency (RF) signal. The RF signals are then amplified by power amplifier (PA) 114 and transmitted to the receiver 104. The receiver amplifies its received RF signals with low noise amplifier (LNA) 116 and downconverts these signals with a demodulator (which generally comprises misers 106-3 and 106-4 and phase adjustment circuitry 108-2) and local oscillator 110-2 so as to generate I and Q signals for the baseband circuitry 112-2.
One issue with this arrangement is that it is difficult to have matching local oscillator signals (from local oscillators 110-1 and 110-2). If there is a difference in frequency the constellation can rotate; an example of which can be seen in FIG. 2, where there is a constellation rotation of a 4-QAM (quadrature amplitude modulation) system. This frequency difference is known as a carrier frequency offset, and, in conventional RF communications systems, carrier frequency offset compensation is usually accomplished by rotating the received baseband constellation (in the digital domain). Performing such digital compensation, however, can be impractical in ultrahigh bandwidth systems (such as millimeter wave or terahertz systems). Therefore, there is a need for analog low cost carrier frequency offset compensation in ultrahigh bandwidth systems.
Some examples of conventional systems are: U.S. Pat. No. 4,166,274; and Gooch et al., “The CM Array: An Adaptive Beamformer for Constant Modulus Signals,” 1986 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '86), April 1986, pp. 2523-2526.